Year: 2022

Shape-Changing Trust-Region Methods Using Multipoint Symmetric Secant Matrices

  • Johannes Brust
  • Jennifer B. Erway
  • Roummel F. Marcia
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , , ,

    In this work, we consider methods for large-scale and nonconvex unconstrained optimization. We propose a new trust-region method whose subproblem is defined using a so-called “shape-changing” norm together with densely-initialized multipoint symmetric secant (MSS) matrices to approximate the Hessian. Shape-changing norms and dense initializations have been successfully used in the context of traditional quasi Newton … Read more

    A Machine Learning Approach to Solving Large Bilevel and Stochastic Programs: Application to Cycling Network Design

  • Bo Lin
    • Categories Integer Programming, Stochastic Programming, Transportation Tags , , , ,

    We present a novel machine learning-based approach to solving bilevel programs that involve a large number of independent followers, which as a special case include two-stage stochastic programming. We propose an optimization model that explicitly considers a sampled subset of followers and exploits a machine learning model to estimate the objective values of unsampled followers. … Read more

    Optimized convergence of stochastic gradient descent by weighted averaging

  • Melinda Hagedorn
  • Florian Jarre
    • Categories Convex Optimization, Data Science Theory, Stochastic Approaches Tags , , , , ,

    Under mild assumptions stochastic gradient methods asymptotically achieve an optimal rate of convergence if the arithmetic mean of all iterates is returned as an approximate optimal solution. However, in the absence of stochastic noise, the arithmetic mean of all iterates converges considerably slower to the optimal solution than the iterates themselves. And also in the … Read more

    A Jacobi-type Newton method for Nash equilibrium problems with descent guarantees

  • Luís Felipe Bueno
  • Gabriel Haeser
  • Oliver Kolossoski
    • Categories Game Theory, Other Topics Tags , , , , ,

    A common strategy for solving an unconstrained two-player Nash equilibrium problem with continuous variables is applying Newton’s method to the system of nonlinear equations obtained by the corresponding first-order necessary optimality conditions. However, when taking into account the game dynamics, it is not clear what is the goal of each player when considering that they … Read more

    Optimizing Vaccine Distribution in Developing Countries under Natural Disaster Risk

  • Bonn Kleiford Seranilla
  • Nils Löhndorf
    • Categories (Mixed) Integer Linear Programming, Dynamic Programming, Stochastic Programming Tags , , ,

    For many developing countries, COVID-19 vaccination roll-out programs are not only slow but vaccination centers are also exposed to the risk of natural disaster, like flooding, which may slow down vaccination progress even further. Policy-makers in developing countries therefore seek to implement strategies that hedge against distribution risk in order for vaccination campaigns to run … Read more

    Water Finds its Level: A Localized Method for Multicommodity Flow Problem

  • Pengfei Liu
    • Categories Network Optimization Tags , , , ,

    This paper describes a local-control method for multicommodity flow problem. Both the capacity constraints and the flow conservation constraints are relaxed. If the flow exceeds the capacity on an edge, the edge would have a congestion cost. If the flow into a vertex is not equal to that out of the vertex, the vertex would … Read more

    Decarbonizing OCP

  • Dimitris Bertsimas
  • Ryan Cory-Wright
  • Vassilis Digalakis Jr
    • Categories Applications - OR and Management Sciences, Production and Logistics, Robust Optimization

    Problem definition: We present our collaboration with the OCP Group, one of the world’s largest producers of phosphate and phosphate-based products, in support of a green initiative designed to reduce OCP’s carbon emissions significantly. We study the problem of decarbonizing OCP’s electricity supply by installing a mixture of solar panels and batteries to minimize its … Read more

    On solving the Cross-dock Door Assignment Problem, CDAP

  • Laureano F. Escudero
  • M. Araceli Garin
  • Aitziber Unzueta
    • Categories Applications - OR and Management Sciences, Production and Logistics Tags , , , ,

    A class of strong lower bounds on the solution value of a Linearized Integer Programming (LIP) reformulation is introduced for the binary quadratic optimization model to assign origin and destination nodes to strip and stack doors, resp., in a cross-dock infrastructure, whose goal is to minimize the transportation cost of the commodities to be handled … Read more

    Computational complexity of decomposing a symmetric matrix as a sum of positive semidefinite and diagonal matrices

  • Levent Tunçel
  • Stephen A. Vavasis
  • jingye xu
    • Categories Finance and Economics, Statistics Tags

    We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades. On the one hand, we prove that when the rank of the positive semidefinite matrix in the decomposition … Read more

    Dynamic Rebalancing Optimization for Bike-sharing Systems: A Modeling Framework and Empirical Comparison

  • Jiaqi Liang
  • Sanjay Dominik Jena
  • Andrea Lodi
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Transportation Tags , , ,

    Bike-sharing systems have been implemented in multiple major cities, offering a low-cost and environmentally friendly transportation alternative to vehicles. Due to the stochastic nature of customer trips, stations are often unbalanced, resulting in unsatisfied demand. As a remedy, operators employ trucks to rebalance bikes among unbalanced stations. Given the complexity of the dynamic rebalancing planning, … Read more